## Abstract In this paper we define the forcing relation and prove its basic properties in the context of the theory ZFCA, i.e., ZFC minus the Foundation axiom and plus the Anti‐Foundation axiom (AFA).
The Bounded Axiom A Forcing Axiom
✍ Scribed by Thilo Weinert
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 138 KB
- Volume
- 56
- Category
- Article
- ISSN
- 0044-3050
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✦ Synopsis
Abstract
We introduce the Bounded Axiom A Forcing Axiom (BAAFA). It turns out that it is equiconsistent with the existence of a regular ∑~2~‐correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom (BPFA) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
📜 SIMILAR VOLUMES
## Abstract We introduce a new simple way of defining the forcing method that works well in the usual setting under FA, the Foundation Axiom, and moreover works even under Aczel's AFA, the Anti‐Foundation Axiom. This new way allows us to have an intuition about what happens in defining the forcing
We study the theories IV,, LV, and overspill principles for 0, formulas. We show that IE, LV, j IV,, but we do not know if IV, j LVn. We introduce a new scheme, the growth scheme Crr, and we prove that LV, CrVn \* IV,. Also, we analyse the utility of bounded collection axioms for the study of the ab